量子计算博士职位

PhD Position F/M Determinism and circuit extraction beyond flow

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Contract type : Fixed-term contract

Level of qualifications required : Graduate degree or equivalent

Fonction : PhD Position

Context

Over the last years, there has been significant progress in quantum computing, on both the theoretical and practical sides. The first experimental demonstrations of quantum error correction provide evidence that large-scale quantum computing will be achievable. Nevertheless, quantum computational resources will remain limited for some time to come. It is therefore important to minimise use of these resources through optimising quantum computations and developing efficient quantum error-correcting codes.

Different approaches to implementing quantum computations are being pursued in parallel. The most widely-used approach is that of quantum circuits, a generalisation of classical logic circuits. Another approach is the one-way model of measurement-based quantum computing, which exploits quantum entanglement and the property that quantum measurements change the state being measured. Measurement-based quantum computing has advantages on both the theoretical and experimental side: for example it links well with quantum error correction, which also makes use of successive quantum measurements. At the same time, measurement-based quantum computing brings new challenges: for example, quantum measurements are generally non-deterministic and care is therefore needed to construct a deterministic computation out of these non-deterministic operations. Flow properties mathematically certify that a measurement-based computation is deterministic in a suitable sense known as ‘robust determinism’. Translation between different models of quantum computing (such as quantum circuits or the one-way model) are necessary to ensure that computations can be implemented on any desired physical quantum computer. They have also shown themselves highly useful for optimisation as certain kinds simplifications are easier to perform in one model than another.

Yet while translation from circuits to the measurement-based model is easy, translation in the other direction – known as ‘circuit extraction’ – is computationally hard in general [3]. At the same time, polynomial-time circuit extraction algorithms are know for measurement-based computations with flow [4, 1, 6]. A recent completeness result for flow-preserving rewriting proved that, starting from a computation with flow, it is possible to locally optimise or modify this computation while preserving both the overall effect and the existence of flow [2]. Simultaneously, the definition of a new property called ZX-flow [5] showed that it is possible to generalise the class of computations for which efficient circuit extraction is possible beyond those that are robustly deterministic.

Assignment

The goal of this thesis is to explore how the definition of robust determinism can be weakened while keeping circuit extraction efficient. A first step would be to find one (or more) ways of characterising how far a computation is from having flow. These characterisations will then be used to find ways of transforming computations that are ‘close’ to having flow into computations with flow. Next, the candidate will generalise the set of flow-preserving rewrite rules by looking for rules that do not increase the new notion of distance. The graphical formalism called ZX-calculus may be useful for these tasks.

A second step is to apply these techniques to quantum error correcting codes and fault-tolerant quantum computation on encoded data. Both the one-way model and error-correcting codes distinguish physical qubits and logical qubits: in the former case, the logical qubits are given by the flow whereas in the latter case they represent the encoded data. The candidate will develop a unified description that can handle both measurement-based quantum computing and quantum error correction with their different approaches to measurement and corrections, as well as the physical-logical distinction.

References

[1] Miriam Backens, Hector Miller-Bakewell, Giovanni de Felice, Leo Lobski & John van de Wetering (2021): There and back again: A circuit extraction tale. Quantum 5, p. 421, doi:10.22331/q-2021-03-25-421. [2] Miriam Backens & Simon Perdrix (2026): Completeness for Flow-Preserving Rewrite Rules, arXiv:2608.13035. [3] N. de Beaudrap, Aleks Kissinger & John van de Wetering (2022): Circuit Extraction for ZX-Diagrams Can Be #P-Hard. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022), Dagstuhl, Germany, pp. 119:1–119:19, doi:10.4230/LIPIcs.ICALP.2022.119. [4] Ross Duncan, Aleks Kissinger, Simon Perdrix & John van de Wetering (2020): Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus. Quantum 4, p. 279, doi:10.22331/q-2020-06-04-279. [5] Aleks Kissinger & John van de Wetering (2026): ZX-Flow: A Flexible Criterion for Deterministic Computation with ZX-Diagrams. arXiv:2603.09580. [6] Will Simmons (2021): Relating Measurement Patterns to Circuits via Pauli Flow. Electronic Proceedings in Theoretical Computer Science 343, pp. 50–101, doi:10.4204/EPTCS.343.4.

Main activities

The candidate will:

• Familiarise themself with the relevant literature

• Develop new formal descriptions of flow

• Prove properties related to these descriptions

Skills

The candidate must have a background in at least one of the fields relevant to theoretical quantum computing: computer science, physics, or mathematics. Previous knowledge of quantum computing is advantageous but not required.

Benefits package

• Subsidized meals

• Partial reimbursement of public transport costs

• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)

• Possibility of teleworking (after 6 months of employment) and flexible organization of working hours

• Professional equipment available (videoconferencing, loan of computer equipment, etc.)

• Social, cultural and sports events and activities

• Access to vocational training

• Social security coverage

Remuneration

€2300 gross/month

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General Information

• Theme/Domain : Proofs and Verification

• Town/city : Villers lès Nancy

• Inria Center :

Centre Inria de l'Université de Lorraine

• Starting date : 2027-01-01

• Duration of contract : 3 years

• Deadline to apply : 2026-10-25

Warning : you must enter your e-mail address in order to save your application to Inria. Applications must be submitted online on the Inria website. Processing of applications sent from other channels is not guaranteed.

Instruction to apply

Defence Security :

This position is likely to be situated in a restricted area (ZRR), as defined in Decree No. 2011-1425 relating to the protection of national scientific and technical potential (PPST).Authorisation to enter an area is granted by the director of the unit, following a favourable Ministerial decision, as defined in the decree of 3 July 2012 relating to the PPST. An unfavourable Ministerial decision in respect of a position situated in a ZRR would result in the cancellation of the appointment.

Recruitment Policy :

As part of its diversity policy, all Inria positions are accessible to people with disabilities.

Contacts

• Inria Team :

MOCQUA

• PhD Supervisor :

Backens Miriam / miriam.backens@inria.fr

About Inria

Inria, the French national institute for research in digital science and technology, supports the French government in national research and innovation strategies in the digital field, acting as Digital Programs Agency. Inria leads over 300 research and innovation projects with its 3,500 scientists, engineers, and support staff, in partnership with universities and the digital ecosystem (businesses, entrepreneurs, and public stakeholders). Together, we explore strategic fields such as artificial intelligence, cybersecurity, quantum computing, cloud technologies, digital transformation in healthcare, digital twins, and digital technologies for defence. We develop practical solutions such as software, tech startups, partnerships with national companies, and cutting-edge training programmes. Our goal is to drive scientific, technological, and industrial excellence to ensure France’s digital sovereignty.